Ramsey Theory : : Unsolved Problems and Results / / Xiaodong Xu, Meilian Liang, Haipeng Luo.
Key problems and conjectures have played an important role in promoting the development of Ramsey theory, a field where great progress has been made during the past two decades, with some old problems solved and many new problems proposed. The present book will be helpful to readers who wish to lear...
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Xu, Xiaodong, author. aut http://id.loc.gov/vocabulary/relators/aut Ramsey Theory : Unsolved Problems and Results / Xiaodong Xu, Meilian Liang, Haipeng Luo. Berlin ; Boston : De Gruyter, [2018] ©2018 1 online resource (XII, 178 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Preface -- Contents -- 1. Some Definitions And Notations -- 2. Ramsey Theory -- 3. Bi-Color Diagonal Classical Ramsey Numbers -- 4. Paley Graphs And Lower Bounds For R(K, K) -- 5. Bi-Color Off-Diagonal Classical Ramsey Numbers -- 6. Multicolor Classical Ramsey Numbers -- 7. Generalized Ramsey Numbers -- 8. Folkman Numbers -- 9. The Erdős–Hajnal Conjecture -- 10. Other Ramsey-Type Problems In Graph Theory -- 11. On Van Der Waerden Numbers And Szemerédi’S Theorem -- 12. More Problems Of Ramsey Type In Additive Number Theory -- 13. Sidon–Ramsey Numbers -- 14. Games In Ramsey Theory -- 15. Local Ramsey Theory -- 16. Set-Coloring Ramsey Theory -- 17. Other Problems And Conjectures -- Epilogue -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Key problems and conjectures have played an important role in promoting the development of Ramsey theory, a field where great progress has been made during the past two decades, with some old problems solved and many new problems proposed. The present book will be helpful to readers who wish to learn about interesting problems in Ramsey theory, to see how they are interconnected, and then to study them in depth. This book is the first problem book of such scope in Ramsey theory. Many unsolved problems, conjectures and related partial results in Ramsey theory are presented, in areas such as extremal graph theory, additive number theory, discrete geometry, functional analysis, algorithm design, and in other areas. Most presented problems are easy to understand, but they may be difficult to solve. They can be appreciated on many levels and by a wide readership, ranging from undergraduate students majoring in mathematics to research mathematicians. This collection is an essential reference for mathematicians working in combinatorics and number theory, as well as for computer scientists studying algorithms. ContentsSome definitions and notationsRamsey theoryBi-color diagonal classical Ramsey numbersPaley graphs and lower bounds for R(k, k)Bi-color off-diagonal classical Ramsey numbersMulticolor classical Ramsey numbersGeneralized Ramsey numbersFolkman numbersThe Erdős–Hajnal conjecture Other Ramsey-type problems in graph theory On van der Waerden numbers and Szemeredi’s theorem More problems of Ramsey type in additive number theory Sidon–Ramsey numbers Games in Ramsey theory Local Ramsey theory Set-coloring Ramsey theory Other problems and conjectures Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Combinatorial analysis. Graph theory. Ramsey theory. Liang, Meilian, author. aut http://id.loc.gov/vocabulary/relators/aut Luo, Haipeng, author. aut http://id.loc.gov/vocabulary/relators/aut University of Science & Technology,. Xu, Xiaodong, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 9783110719550 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English 9783110604252 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 9783110603255 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 English 9783110604191 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 9783110603194 ZDB-23-DMA EPUB 9783110576634 print 9783110576511 https://doi.org/10.1515/9783110576702 https://www.degruyter.com/isbn/9783110576702 Cover https://www.degruyter.com/cover/covers/9783110576702.jpg |
language |
English |
format |
eBook |
author |
Xu, Xiaodong, Xu, Xiaodong, Liang, Meilian, Luo, Haipeng, |
spellingShingle |
Xu, Xiaodong, Xu, Xiaodong, Liang, Meilian, Luo, Haipeng, Ramsey Theory : Unsolved Problems and Results / Frontmatter -- Preface -- Contents -- 1. Some Definitions And Notations -- 2. Ramsey Theory -- 3. Bi-Color Diagonal Classical Ramsey Numbers -- 4. Paley Graphs And Lower Bounds For R(K, K) -- 5. Bi-Color Off-Diagonal Classical Ramsey Numbers -- 6. Multicolor Classical Ramsey Numbers -- 7. Generalized Ramsey Numbers -- 8. Folkman Numbers -- 9. The Erdős–Hajnal Conjecture -- 10. Other Ramsey-Type Problems In Graph Theory -- 11. On Van Der Waerden Numbers And Szemerédi’S Theorem -- 12. More Problems Of Ramsey Type In Additive Number Theory -- 13. Sidon–Ramsey Numbers -- 14. Games In Ramsey Theory -- 15. Local Ramsey Theory -- 16. Set-Coloring Ramsey Theory -- 17. Other Problems And Conjectures -- Epilogue -- Bibliography -- Index |
author_facet |
Xu, Xiaodong, Xu, Xiaodong, Liang, Meilian, Luo, Haipeng, Liang, Meilian, Liang, Meilian, Luo, Haipeng, Luo, Haipeng, University of Science & Technology,. Xu, Xiaodong, Xu, Xiaodong, |
author_variant |
x x xx x x xx m l ml h l hl |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Liang, Meilian, Liang, Meilian, Luo, Haipeng, Luo, Haipeng, University of Science & Technology,. Xu, Xiaodong, Xu, Xiaodong, |
author2_variant |
m l ml h l hl o s t u ost ostu x x xx x x xx |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn TeilnehmendeR MitwirkendeR MitwirkendeR |
author_sort |
Xu, Xiaodong, |
title |
Ramsey Theory : Unsolved Problems and Results / |
title_sub |
Unsolved Problems and Results / |
title_full |
Ramsey Theory : Unsolved Problems and Results / Xiaodong Xu, Meilian Liang, Haipeng Luo. |
title_fullStr |
Ramsey Theory : Unsolved Problems and Results / Xiaodong Xu, Meilian Liang, Haipeng Luo. |
title_full_unstemmed |
Ramsey Theory : Unsolved Problems and Results / Xiaodong Xu, Meilian Liang, Haipeng Luo. |
title_auth |
Ramsey Theory : Unsolved Problems and Results / |
title_alt |
Frontmatter -- Preface -- Contents -- 1. Some Definitions And Notations -- 2. Ramsey Theory -- 3. Bi-Color Diagonal Classical Ramsey Numbers -- 4. Paley Graphs And Lower Bounds For R(K, K) -- 5. Bi-Color Off-Diagonal Classical Ramsey Numbers -- 6. Multicolor Classical Ramsey Numbers -- 7. Generalized Ramsey Numbers -- 8. Folkman Numbers -- 9. The Erdős–Hajnal Conjecture -- 10. Other Ramsey-Type Problems In Graph Theory -- 11. On Van Der Waerden Numbers And Szemerédi’S Theorem -- 12. More Problems Of Ramsey Type In Additive Number Theory -- 13. Sidon–Ramsey Numbers -- 14. Games In Ramsey Theory -- 15. Local Ramsey Theory -- 16. Set-Coloring Ramsey Theory -- 17. Other Problems And Conjectures -- Epilogue -- Bibliography -- Index |
title_new |
Ramsey Theory : |
title_sort |
ramsey theory : unsolved problems and results / |
publisher |
De Gruyter, |
publishDate |
2018 |
physical |
1 online resource (XII, 178 p.) |
contents |
Frontmatter -- Preface -- Contents -- 1. Some Definitions And Notations -- 2. Ramsey Theory -- 3. Bi-Color Diagonal Classical Ramsey Numbers -- 4. Paley Graphs And Lower Bounds For R(K, K) -- 5. Bi-Color Off-Diagonal Classical Ramsey Numbers -- 6. Multicolor Classical Ramsey Numbers -- 7. Generalized Ramsey Numbers -- 8. Folkman Numbers -- 9. The Erdős–Hajnal Conjecture -- 10. Other Ramsey-Type Problems In Graph Theory -- 11. On Van Der Waerden Numbers And Szemerédi’S Theorem -- 12. More Problems Of Ramsey Type In Additive Number Theory -- 13. Sidon–Ramsey Numbers -- 14. Games In Ramsey Theory -- 15. Local Ramsey Theory -- 16. Set-Coloring Ramsey Theory -- 17. Other Problems And Conjectures -- Epilogue -- Bibliography -- Index |
isbn |
9783110576702 9783110719550 9783110604252 9783110603255 9783110604191 9783110603194 9783110576634 9783110576511 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA166 |
callnumber-sort |
QA 3166 X865 42018 |
url |
https://doi.org/10.1515/9783110576702 https://www.degruyter.com/isbn/9783110576702 https://www.degruyter.com/cover/covers/9783110576702.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
511 - General principles of mathematics |
dewey-full |
511/.66 |
dewey-sort |
3511 266 |
dewey-raw |
511/.66 |
dewey-search |
511/.66 |
doi_str_mv |
10.1515/9783110576702 |
oclc_num |
1048948547 |
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